Section: Software

Mathematics on the Web

We also provide access to our work to scientists who are not using Maple or any other computer algebra system in the form of automatically generated encyclopedias available on the web. The Encyclopedia of Combinatorial Structures at http://algo.inria.fr/ecs/ thus contains more than 1000 combinatorial structures for which generating functions, enumeration sequences, recurrences, and asymptotic approximations have been computed automatically. It gets more than 16,000 hits per month. The Dynamic Dictionary of Mathematical Functions (DDMF) at http://ddmf.msr-inria.inria.fr/ gathers several dozens of special functions for which identities, guaranteed high-precision numerical evaluations, power-series and asymptotic expansions, graphs, ...are generated automatically and on the user's request, starting from a linear differential equation and its initial conditions. The underlying symbolic algorithms and implementations are those of gfun and Mgfun. All the production process being automated, the difficult and expensive step of checking each formula individually is suppressed. A nice specificity of this encyclopedia is its interactivity: the approximations values (numbers, series) are not bound to a statically set precision, rather, the user can fill in the precision he wants in a form, before clicking to ask for a refined identity to be generated, then displayed. This interactivity is based on a tool DynaMoW at http://ddmf.msr-inria.inria.fr/DynaMoW/ (for Dynamic Mathematics on the Web) that we develop as well. This is an Ocaml library that simultaneously controls external symbolic calculations and web-page generation at the same time. Being available on the web, the DDMF also plays the role of a showcase for part of the packages developed in our project. It is a successor of our former Encyclopedia of Special Functions at http://algo.inria.fr/esf/ .